Numerical study of nanofluid mixed convection in a horizontal curved tube using two-phase approach

Laminar mixed convection of nanofluid consisting of water/Al₂O₃ in a horizontal curved tube is investigated numerically. Three dimensional elliptical governing equations have been solved to study the simultaneous effect of the buoyancy and centrifugal forces throughout the curved tube. The effects of nanoparticle concentrations on the secondary flow and also on the contours of temperature are presented and discussed. Axial velocity profiles with respect to the horizontal and vertical diameter are shown. In addition, the effects of nanoparticle volume fractions on the axial evolution of the local peripheral average convective heat transfer coefficient and the local peripheral average skin friction coefficient are studied. It is shown that the average convective heat transfer coefficient augments with the nanoparticle concentrations. However, its effect on the average skin friction coefficient is negligible.     

Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load

A network of polymers can imbibe a large quantity of a solvent and swell, resulting in a gel. The swelling process can be markedly influenced by a mechanical load and geometric constraint. When the network, solvent, and mechanical load equilibrate, inside the gel the chemical potential of the solvent is homogeneous, but the concentration of the solvent and the deformation of the network can be inhomogeneous. We use the chemical potential of the solvent and the deformation gradient of the network as the independent variables of the free-energy function, and show that the boundary value problem of the swollen gel is equivalent to that of a hyperelastic solid. We implement this approach in the finite-element package, ABAQUS, and analyze examples of swelling-induced deformation, contact, and bifurcation. Because commercial software like ABAQUS is widely available, this work may provide a powerful tool to study complex phenomena in gels.     

Natural convection of an alumina-water nanofluid inside an inclined wavy-walled cavity with a non-uniform heating using Tiwari and Das' nanofluid model

The present study is devoted to numerical analysis of natural convective heat transfer and fluid flow of alumina-water nanofluid in an inclined wavy-walled cavity under the effect of non-uniform heating. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been included in the mathematical model. The considered governing equations formulated in dimensionless stream function, vorticity, and temperature have been solved by the finite difference method. The cavity inclination angle and irregular walls(wavy and undulation numbers)are very good control parameters for the heat transfer and fluid flow. Nowadays, optimal parameters are necessary for the heat transfer enhancement in different practical applications. The effects of the involved parameters on the streamlines and isotherms as well as on the average Nusselt number and nanofluid flow rate have been analyzed. It has been found that the heat transfer rate and fluid flow rate are non-monotonic functions of the cavity inclination angle and undulation number.     

The bubble fossil record: insight into boiling nucleation using nanofluid pool-boiling

Subcooled pool boiling of Al₂O₃/water nanofluid (0.1 vol%) was investigated. Scanning electron microscopy and energy dispersive X-ray spectroscopy were used to observe surface features of the wire heater where nanoparticles had deposited. A layer of aggregated alumina particles collected on the heated surface, where evidence of fluid shear associated with bubble nucleation and departure was “fossilized” in the fluidized nano-porous surface coating. These structures contain evidence of the fluid forces present in the microlayer prior to departure and provide a unique understanding of boiling phenomena. A unique mode of heat transfer was identified in nanofluid pool boiling.     

Turbulent forced convection of nanofluid in a wavy channel using two phase model

Two phase mixture model is used to numerically simulate the turbulent forced convection of Al₂O₃-Water nanofluid in a channel with corrugated wall under constant heat flux. Both mixture and single phase models are implemented to study the nanofluid flow in such a geometry and the results have been compared. The effects of the volume fraction of nanoparticles, Reynolds number and amplitude of the wavy wall on the rate of heat transfer are investigated. The results showed that with increasing the volume fraction of nanoparticles, Reynolds number and amplitude of wall waves, the rate of heat transfer increases. Also the results showed that the mixture model yields to higher Nusselt numbers than the single phase model in a similar case.     

A solution of transport in porous media with equilibrium and kinetic reactions

A solution is presented to verify numerical computer codes of reactive transport with both equilibrium and kinetic reactions. A synthetic model of A ↔ B ↔ C → chain reactions is proposed to describe operator-splitting numerical schemes used in numerical computer codes. A reaction matrix is derived for both the equilibrium and the first-order kinetic reactions and further decoupled as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the reaction matrix can be transformed into independent PDEs, for which closed-form solutions exist or can be derived. The solution derived in this study is compared with numerical results.     

Gas absorption in a thin liquid film flow on a horizontal rotating disk

An analytical model for the rate of gas absorption into laminar non-wavy film flow on a horizontal rotating disk is obtained assuming short contact times. Literature data for the oxygen mass transfer coefficient in a wavy film is correlated by means of the dimensionless numbers deriving from the model. The rate enhancement due to waves is found to vary from 6 to 13 times. It is established that the absorption process in the film on the disk as compared to that in a gravitational wavy film flow can be intensified up to 14 times by means of a moderate rotation speed.     

The onset of convection in a nanofluid saturated porous layer using Darcy model with cross diffusion

Linear and nonlinear stability analysis for the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. In conjunction with the Brownian motion, the nanoparticle fraction becomes stratified, hence the viscosity and the conductivity are stratified. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation, in the vertical direction, of conductivity and viscosity. The critical Rayleigh number, wave number for stationary and oscillatory mode and frequency of oscillations are obtained analytically using linear theory and the non-linear analysis is made with minimal representation of the truncated Fourier series analysis involving only two terms. The effect of various parameters on the stationary and oscillatory convection is shown pictorially. We also study the effect of time on transient Nusselt number and Sherwood number which is found to be oscillatory when time is small. However, when time becomes very large both the transient Nusselt value and Sherwood value approaches to their steady state values.     

Unsteady heat and mass transfer in a rotating nanofluid layer

The present paper studies the effect of rotation on the thermal instability in a horizontal layer of a Newtonian nanofluid which incorporates the effect of Brownian motion along with thermophoresis. In order to find the concentration and the thermal Nusselt numbers for unsteady state, a nonlinear analysis, using a minimal representation of the truncated Fourier series of two terms, has been performed. The results obtained are then presented graphically. It is observed that rotation delays the rate of heat and mass transferred, representing a delay in the onset on convection. This shows a stabilizing effect for a rotating system against a nonrotating system.     

Heat transfer mechanism of miniature loop heat pipe with water-copper nanofluid: thermodynamics model and experimental study

In order to ensure the normal work of electronic product, the thermal management is of key importance. Miniature loop heat pipe (mLHP) is a promising device of heat transfer for electronic products. Cu-water nanofluid with different concentration is used as working material in mLHP. Experiments are conducted to investigate its heat transfer performance. The heat flux owing to thermal diffusion is calculated. It is found that this heat flux and the boiling temperature are non-monotonic function of concentration of nanoparticle. Turning concentration appears at about 1.5 wt%. Differential equation of thermal diffusion produced by micro movement of nanoparticle is established in this paper. Average speed formula for nanoparticles is derived and slope of the curve of phase equilibrium is obtained. Based on the theoretical research in this paper, enhanced heat transfer mechanism of nanofluid is analyzed. The facts that heat flux owing to thermal diffusion and boiling temperature are all associated with nanoparticle concentration are also well explained with the aid of the derived theory in this paper.     

Investigating the diameter of solid particles effects on a laminar nanofluid flow in a curved tube using a two phase approach

In this paper, we report the results of our numerical studies on laminar mixed convection heat transfer in a circular Curved tube with a nanofluid consisting of water and 1 vol.% Al₂O₃. Three dimensional elliptic governing equations have been used. Two phase mixture model and control volume technique have been implemented to study flow field. Effects of the diameter of particles on the hydrodynamic and thermal parameters are investigated and discussed. Increasing the solid particles diameter decreases the Nusselt number and secondary flow, while the axial velocity augments. When the particles are in order of nano meter, increasing the diameter of particles, do not change the flow behaviors. The distribution of solid nanoparticles is uniform and constant in curved tube.     

Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

Measurement of liquid film thickness using a laser light absorption method

A photometric technique for film thickness measurements is described in this paper. It is based on the absorption of light passing through a layer of dyed liquid and takes advantage of small sized diode laser sources and sensitive light sensors. The method is non-intrusive, easy to use and to calibrate and can be implemented at relatively low cost. Laboratory tests of the technique have yielded satisfactory accuracy and repeatability. Moreover, the technique allows measurements with a good spatial resolution. Flowing film thickness measurements made photometrically are compared directly to measurements taken simultaneously with a “parallel wire conductance probe”. Time-averaged film heights, RMS values and other statistical information have been obtained by analyzing these instantaneous film thickness records. With regard to the time-averaged values of liquid film thickness, there is a satisfactory agreement between the two measuring techniques. Received: 11 February 1999/Accepted: 30 May 1999     

Modeling droplet dispersion and interphase turbulent kinetic energy transfer using a new dual-timescale Langevin model

Dispersion of spray droplets and the modulation of turbulence in the ambient gas by the dispersing droplets are two coupled phenomena that are closely linked to the evolution of global spray characteristics, such as the spreading rate of the spray and the spray cone angle. Direct numerical simulations (DNS) of turbulent gas flows laden with sub-Kolmogorov size particles, in the absence of gravity, report that dispersion statistics and turbulent kinetic energy (TKE) evolve on different timescales. Furthermore, each timescale behaves differently with Stokes number, a non-dimensional flow parameter (defined in this context as the ratio of the particle response time to the Kolmogorov timescale of turbulence) that characterizes how quickly a particle responds to turbulent fluctuations in the carrier or gas phase. A new dual-timescale Langevin model (DLM) composed of two coupled Langevin equations for the fluctuating velocities, one for each phase, is proposed. This model possesses a unique feature that the implied TKE and velocity autocorrelation in each phase evolve on different timescales. Consequently, this model has the capability of simultaneously predicting the disparate Stokes number trends in the evolution of dispersion statistics, such as velocity autocorrelations, and TKE in each phase. Predictions of dispersion statistics and TKE from the new model show good agreement with published DNS of non-evaporating and evaporating droplet-laden turbulent flow.     

Experimental study of critical heat flux enhancement during forced convective flow boiling of nanofluid on a short heated surface

Enhancements of nucleate boiling critical heat flux (CHF) using nanofluids in a pool boiling are well-known. Considering importance of flow boiling heat transfer in various practical applications, an experimental study on CHF enhancements of nanofluids under convective flow conditions was performed. A rectangular flow channel with 10-mm width and 5-mm height was used. A 10 mm-diameter disk-type copper surface, heated by conduction heat transfer, was placed at the bottom surface of the flow channel as a test heater. Aqueous nanofluids with alumina nanoparticles at the concentration of 0.01% by volume were investigated. The experimental results showed that the nanofluid flow boiling CHF was distinctly enhanced under the forced convective flow conditions compared to that in pure water. Subsequent to the boiling experiments, the heater surfaces were examined with scanning electron microscope and by measuring contact angle. The surface characterization results suggested that the flow boiling CHF enhancement in nanofluids is mostly caused by the nanoparticles deposition of the heater surface during vigorous boiling of nanofluids and the subsequent wettability enhancements.     

Heat transfer enhancement using Al2O3/water nanofluid in a two-phase closed thermosyphon

A two-phase closed thermosyphon (TPCT) is a device for heat transmission. It consists of an evacuated-close tube filled with a certain amount of working fluid. Fluids with nanoparticles (particles smaller than 100 nm) suspended in them are called nanofluids that they have a great potential in heat transfer enhancement. In the present study, we combined two mentioned techniques for heat transfer enhancement. Nanofluids of aqueous Al₂O₃ nanoparticles suspensions were prepared in various volume concentration of 1–3% and used in a TPCT as working media. Experimental results showed that for different input powers, the efficiency of the TPCT increases up to 14.7% when Al₂O₃/water nanofluid was used instead of pure water. Temperature distributions on TPCT confirm these results too.     

MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions

The steady laminar magnetohydrodynamic mixed convection boundary layer flow of a nanofluid near the stagnation-point on a vertical permeable plate with prescribed external flow and surface temperature is investigated in this study. Here, both assisting and opposing flows are considered and studied. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved numerically using the Runge–Kutta scheme coupled with a conventional shooting procedure. Three different types of nanoparticles, namely copper Cu, alumina Al₂O₃ and titania TiO₂ with water as the base fluid are considered. Numerical results are obtained for the skin-friction coefficient and Nusselt number as well as for the velocity and temperature profiles for some values of the governing parameters, namely, the volume fraction of nanoparticles ?, permeability parameter f _o , magnetic parameter M and mixed convection parameter λ. It is found that dual solutions exist for both assisting and opposing flows, and the range of the mixed convection parameter for which the solution exists, increases with suction, magnetic field and volume fraction of nanoparticles.     

Solution of internal problems of aerodynamics under transitional conditions using a model kinetic equation

A method is developed based on the use of a model kinetic equation with a shock frequency = v/l (l is the mean length of the free flight path; v is the modulus of the molecular velocity). The method is tested on several classical problems.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 23–28, March–April, 1972.